Question

If x+y+z=8x+y+z=8 and x2+y2+z2=50 x 2+y2+z2=50 , then the value of xy+yz+zx xy+yz+zx is

Answer 1

Given,

x + y + z = 8

x² + y² + z² = 50

Find  out :- xy + yx + zx + xy + yz + zx = 2xy+2xz + 2yz

We know that,

(x + y + z)² = x² + y² + z² + 2xy + 2yz +2zx

8² = 50 +  2xy + 2yz +2zx

64 = 50 + 2xy + 2yz +2zx

2xy + 2yz +2zx = 64 - 50

2xy + 2yz + 2zx = 14

xy + yz + zx + xy + yz + zx = 14